State Wien’s displacement law.Wien’s displacement law states that the product of wavelength of maximum emission and the absolute temperature of the body is constant. λmT = constant = 0.2892 cm kAccording to this law, the wavelength of maximum emission decreases with the increase in temperature of the body.

Women's displacement law states that the black body radiation curvefor different temperature peaksat a wavelength inversely proportional to temperature

Wein's Displacement Law:

Wein's Displacement Law, formulated by Wilhelm Wien in 1893, relates the wavelength at which the intensity of radiation emitted by a black body is maximum to its temperature. According to this law, the product of the wavelength (λ) at which the radiation is most intense and the absolute temperature (T) of the black body is a constant value, known as Wien's Displacement Constant (denoted by the symbol, b).

Mathematical Representation:

Mathematically, Wein's Displacement Law can be expressed as:

λ * T = b

Where:
- λ represents the wavelength at which the radiation is most intense.
- T denotes the absolute temperature of the black body.
- b is the Wien's Displacement Constant, which has a value of approximately 2.898 × 10^-3 m·K.

Explanation:

1. Black Body Radiation:
A black body is an idealized object that absorbs all incident radiation without reflecting or transmitting any portion of it. When a black body is heated, it emits electromagnetic radiation over a wide range of wavelengths. The intensity of this radiation varies with the temperature of the black body.

2. Relationship Between Wavelength and Temperature:
Wein's Displacement Law states that as the temperature of a black body increases, the peak intensity of its emitted radiation shifts towards shorter wavelengths. In other words, hotter objects emit more intense radiation at shorter wavelengths. This relationship is crucial in understanding the behavior of thermal radiation.

3. Peak Wavelength and Temperature:
The peak wavelength (λ) at which the radiation intensity is maximum is inversely proportional to the absolute temperature (T) of the black body. As the temperature increases, the peak wavelength decreases. This relationship can be expressed as: λ ∝ 1/T.

4. Wien's Displacement Constant:
The proportionality constant in the relationship between peak wavelength and temperature is the Wien's Displacement Constant (b). It is a fundamental constant in physics and has a fixed value of approximately 2.898 × 10^-3 m·K.

5. Applications:
Wein's Displacement Law finds applications in various fields such as astrophysics, thermodynamics, and the study of black body radiation. It helps determine the temperature of stars based on their emitted radiation spectra and is utilized in infrared technology, including infrared cameras and sensors.

In conclusion, Wein's Displacement Law provides a fundamental understanding of the relationship between the peak wavelength of radiation emitted by a black body and its temperature. This law has wide-ranging applications and has significantly contributed to our knowledge of thermal radiation and the behavior of objects at different temperatures.